Question:
Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6300
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $11403
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are givenFormual to Calculate Simple Interest when Principal and Amount are given
We know that, Amount (A) = Principal (P) + Simple Interest (SI)
⇒ Simple Interest (SI) = Amount – Principal
⇒ SI = $11403 – $6300 = $5103
Thus, Simple Interest = $5103
Calculation of the Time using forumula when Amount, Simple Interest and Principal are known
Formula to find the Time (T)
Time (T) = 100 × Simple Interest/Principal × Rate of Interest
⇒ T = 100 × SI/P × R
Thus, Time (T) = 100 × 5103/6300 × 9
= 510300/56700
= 9 years (using formula)
Thus, Time (T) = 9 years (from time taken before calculation)Answer
Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known
Here, we have
Principal (P) = $6300
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $5103 (As calculated above by subtracting Principal from the Amount given)
We know that, interest is calculated on the basis of the Principal.
This means Simple Interest for 1 year = Rate of simple interest × Principal
Thus, Simple Interest for 1 year = 9% of Principal
= 9% of $6300
= 9/100 × 6300
= 9 × 6300/100
= 56700/100 = 567
Thus, simple Interest for 1 year = $567
Now,
∵ If the simple Interest is $567, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/567 years
∴ If the simple Interest is $5103, then the time = 1/567 × 5103 years
= 1 × 5103/567 years
= 5103/567 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 4 years.
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 4 years.
(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(4) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(5) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10860 to clear the loan, then find the time period of the loan.
(6) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.
(7) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.
(9) If David borrowed $3400 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.